Copper is one of the essential micronutrients utilized as a cofactor in a wide variety of biochemical reactions of metabolic pathways, including mitochondrial respiration and innate immune response. Cellular concentration and distribution of copper is regulated by copper-specific transporters, chaperones, metallothionein proteins and amino acids. Transcription of a major copper metallothionein, CUP1 is epigenetically regulated in Saccharomyces cerevisiae. Mutations in histones dysregulate cellular copper homeostasis due to abnormal epigenetic changes and cause diseases in humans, such as cancerous growth and neurological disorders. Low or higher cellular concentration of copper is associated with disorders such as Menkes and Wilson's disease, respectively. Higher concentrations of copper cause caspase-independent cell death known as cuproptosis and haemolytic anemia. We highlighted the existing knowledge regarding the significance of epigenetics and cellular factors in the regulation of copper metabolism and copper-regulated protein trafficking. We have also proposed a few future directions to explore the role of cellular pH dynamics, stoichiometry among metals, amino acids and protein metabolism, histone modifications, autophagy and mitochondrial respiration in regulating cellular copper metabolism. Altogether, we provide a comprehensive summary of cellular factors targeting copper metabolism for dissecting the underlying complex mechanism of copper dynamics in normal physiology and diseases.